82.

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		2.4.2— Bifurcation Diagrams

		One way to detect a bifurcation is to plot values of one of the variables of the system versus the value of a parameter. This plot is called a bifurcation diagram.

		Each point on the x-axis corresponds to one value of the parameter. Vertically above this parameter is then plotted many values of the variable as the system evolves in time. The y-direction is therefore a smear of all the values of the variable that occur at that value of the parameter on the x-axis. This vertical smear forms a pattern. An abrupt change in the form of this pattern with a small change in the parameter plotted on the x-axis signals the existence of a bifurcation.

		The bifurcation diagram of a chaotic system has fractal features. That is, small regions of the plot have the same structure as larger regions.

 

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